Atmospheric Effects on the Isotopic Composition of Ozone

: The delta values of the isotope composition of atmospheric ozone is ~100‰ (referenced to atmospheric O 2 ). Previous photochemical models, which considered the isotope fractionation processes from both formation and photolysis of ozone, predicted δ 49 O 3 and δ 50 O 3 values, in δ 49 O 3 versus δ 50 O 3 space, that are >10‰ larger than the measurements. We propose that the difference between the model and observations could be explained either by the temperature variation, Chappuis band photolysis, or a combination of the two and examine them. The isotopic fractionation associated with ozone formation increases with temperature. Our model shows that a hypothetical reduction of ~20 K in the nominal temperature proﬁle could reproduce the observations. However, this hypothesis is not consistent with temperatures obtained by in situ measurements and NCEP Reanalysis. Photolysis of O 3 in the Chappuis band causes O 3 to be isotopically depleted, which is supported by laboratory measurements for 18 O 18 O 18 O but not by recent new laboratory data made at several wavelengths for 49 O 3 and 50 O 3 . Cloud reﬂection can signiﬁcantly enhance the photolysis rate and affect the spectral distribution of photons, which could inﬂuence the isotopic composition of ozone. Sensitivity studies that modify the isotopic composition of ozone by the above two mechanisms are presented. We conclude isotopic fractionation occurring in photolysis in the Chappuis band remains the most plausible solution to the model-observation discrepancy. Implications of our results for using the oxygen isotopic signature for constraining atmospheric chemical processes related to ozone, such as CO 2 , nitrate, and the hydroxyl radical, are discussed.

In this paper, we test four processes in six separate models ( Table 1). The Caltech/JPL KINETICS model is used in our study. All models apply the modified zero-point-energy (ZPE) theory [27,28] for the isotopic fractionation in the Hartley and Huggins bands. The four effects considered here include temperature, pressure, photolytic fractionation in the Chappuis band, and cloud scattering. The reference model is one-dimensional (1-D) and considers an altitude-dependent profile of temperature and eddy coefficients, that can best describe globally averaged atmospheric temperature and vertical transport (see [5] and references contained therein for details). The main reason for choosing 1-D, instead of 3-D, is that alteration of ozone normally occurs predominantly in the dayside atmosphere where local photochemical equilibrium is attained. As a result, the fractionation that defines the isotopic composition of atmospheric ozone is affected dominantly by the processes of formation and photolysis, the two main factors explored here. To better compare with the observational data across latitudes in different seasons, we also run 2-D models. The ozone isotope chemistry model is taken from Liang et al. [5], which was built at the low-pressure limit for ozone formation, with modifications (see the following sections). Table 1. List of processes considered in the photochemical models.

Temperature
Pressure Photolysis Cloud Models A-C and E-F use the nominal temperature profile (see Figure 1 of Liang et al. [5]). Reduction in the temperature profile is applied to Model D. Pressure dependence in fractionating the isotopic composition of ozone during its formation is considered in Models A and C-F; the low-pressure limit is assumed in Model B (same as [5]). Due to insufficient data for the isotopic fractionation caused by the photolysis in the Chappuis band, three different calculations are applied. ZPE theory [29] is assumed in Models D-E, and the rest use a laboratory-based calculation. See later sections for details. To check the validity of the adopted fractionations, we compare the calculated values with recently measured numbers at several wavelengths in the Chappuis band [30][31][32].
This paper is divided into five parts. The impacts of pressure, temperature, and Chappuis band photolysis on the isotopic composition of O 3 are examined in Sections 2-4, respectively. A discussion and conclusions follow in Section 5.

Pressure Dependence
In previous calculations [5,6], the low-pressure limit (i.e., stratospheric condition) is emphasized. It is known that the isotopic enrichment of ozone decreases with increasing pressure [33], and hence, we expect that taking into account the pressure-dependence of the isotopic fractionation occurred during ozone formation would help reduce the difference between the model and observations at the surface.
The pressure dependence is weak at pressures less than 100 mbar but becomes significant at a higher pressure. For example, δ 50 O 3 (or enrichment) decreases by~30‰ at pressures from~100 to 1000 mbar [33,34]. We follow Marcus and Gao's model [35][36][37] for the pressure-dependent calculation of each isotope-variant rate coefficient and parameter-ize them following a semi-analytic approach derived by Gao and Marcus [34]; the ozone formation model adopted in this study is the same as that in Liang et al. [5]. (The same approach was also taken previously by Wiegel et al. [23].) We fit the fractionation ε of each rate coefficient at a given temperature by ε = ε 0 /(1 + P/P 1/2 ) where P is the atmospheric pressure and P 1/2 is the pressure at which ε takes one-half of the value of its low-pressure limit ε 0 . Both P 1/2 and ε 0 are isotope-variant and temperaturedependent. The latter is presented by Liang et al. [5], and the functional dependence of P 1/2 is rather complicated; the effective P1/2 of δ 50 [33] and a more sophisticated model [36]. Figure 1 compares the model profile of δ 50 O 3 for cases with (Model A) and without (Model B) the pressuredependence; the temperature profile is the same as that used previously [5]. The surface temperature is 283.4 K and the resulting δ 50 O 3 is~80‰ for Model E, which is much improved over the previous low-pressure limit model [5]. The new value is consistent with tropospheric measurements at similar temperatures [2,8] but inconsistent with Model A because of considering the photolysis-induced isotope fractionation in the Chappuis band (see Section 4). A likely explanation is that the ozone is largely affected by the Leighton cycle (and NO x -CO-VOC-O 3 photochemistry), not the Chapman chemistry for a clean atmosphere we emphasize here. See later sections for further discussion.
pressure [33], and hence, we expect that taking into account the pressure-dependence of the isotopic fractionation occurred during ozone formation would help reduce the difference between the model and observations at the surface.
The pressure dependence is weak at pressures less than 100 mbar but becomes significant at a higher pressure. For example, δ 50 O3 (or enrichment) decreases by ~30‰ at pressures from ~100 to 1000 mbar [33,34]. We follow Marcus and Gao's model [35][36][37] for the pressure-dependent calculation of each isotope-variant rate coefficient and parameterize them following a semi-analytic approach derived by Gao and Marcus [34]; the ozone formation model adopted in this study is the same as that in Liang et al. [5]. (The same approach was also taken previously by Wiegel et al. [23].) We fit the fractionation ε of each rate coefficient at a given temperature by where P is the atmospheric pressure and P1/2 is the pressure at which ε takes one-half of the value of its low-pressure limit ε0. Both P1/2 and ε0 are isotope-variant and temperaturedependent. The latter is presented by Liang et al. [5], and the functional dependence of P1/2 is rather complicated; the effective P1/2 of δ 50 O3 ( 16 [33] and a more sophisticated model [36]. Figure 1 compares the model profile of δ 50 O3 for cases with (Model A) and without (Model B) the pressure-dependence; the temperature profile is the same as that used previously [5]. The surface temperature is 283.4 K and the resulting δ 50 O3 is ~80‰ for Model E, which is much improved over the previous low-pressure limit model [5]. The new value is consistent with tropospheric measurements at similar temperatures [2,8] but inconsistent with Model A because of considering the photolysis-induced isotope fractionation in the Chappuis band (see Section 4). A likely explanation is that the ozone is largely affected by the Leighton cycle (and NOx-CO-VOC-O3 photochemistry), not the Chapman chemistry for a clean atmosphere we emphasize here. See later sections for further discussion.  [5]. Pressure and temperature dependences in O3 isotopic fractionations are taken into account, and the isotopic  Table 1 for model differences. Diamonds are balloon-borne mass spectrometer measurements [3]. The asterisks [8] and triangle [2] are the near-surface measurements. The error bars in the atmospheric measurements are for 1-σ. The experimental data variations represent spatial and temporal differences at which the data were taken.

Temperature Variation
The isotopic fractionation by photolysis has a weak temperature dependence [5,38]. The temperature dependence of the isotopic value (δ) of ozone is primarily from the formation of ozone. The temperature sensitivity for δ in ozone formation is~0.3‰ K −1 , and the value becomes~0.6‰ K −1 after considering O + O 2 isotopic exchange processes [39]. To bring the model δ-values of ozone into better agreement with observations requires a reduction of~15-20 K in the climatological temperature profile (Model D vs. Model E). To refine previous calculations [5,6,22], we examine the effect by replacing the temperature profile used in previous studies with more realistic daily and 6-hourly temperature profiles from the National Centers for Environmental Prediction-Department of Energy Reanalysis 2 (NCEP2) [40].
The zero-point-energy theory for estimating the isotopic fractionation of ozone in the Chappuis band is assumed, as in Liang et al. [5]. Combining the kinetic fractionation processes in the formation and photolysis of ozone, the calculated δ 49 O 3 and δ 50 O 3 remain >10‰ larger than the measurements ( Figure 2). Here, we update previous calculations to include pressure dependence, which reduces δ-values at higher pressures. By incorporating NCEP2 daily temperature into the model, a better agreement is achieved. However, there is a difference between the observed temperature (in situ measurements and NCEP2 data) and the temperature that is required to reproduce the observed values of δ 49 O 3 and δ 50 O 3 (Table 1 and Figure 3). The in situ measured temperature tends to be higher than the climatological and NCEP2 daily and 6-hourly temperature.
fractionation for ozone photolysis in the Chappuis band is scaled from 18 Table 1 for model differences. Diamonds are balloon-borne mass spectrometer measurements [3]. The asterisks [8] and triangle [2] are the near-surface measurements. The error bars in the atmospheric measurements are for 1-σ. The experimental data variations represent spatial and temporal differences at which the data were taken.

Temperature Variation
The isotopic fractionation by photolysis has a weak temperature dependence [5,38]. The temperature dependence of the isotopic value (δ) of ozone is primarily from the formation of ozone. The temperature sensitivity for δ in ozone formation is ~0.3‰ K −1 , and the value becomes ~0.6‰ K −1 after considering O + O2 isotopic exchange processes [39]. To bring the model δ-values of ozone into better agreement with observations requires a reduction of ~15-20 K in the climatological temperature profile (Model D vs. Model E). To refine previous calculations [5,6,22], we examine the effect by replacing the temperature profile used in previous studies with more realistic daily and 6-hourly temperature profiles from the National Centers for Environmental Prediction-Department of Energy Reanalysis 2 (NCEP2) [40].
The zero-point-energy theory for estimating the isotopic fractionation of ozone in the Chappuis band is assumed, as in Liang et al. [5]. Combining the kinetic fractionation processes in the formation and photolysis of ozone, the calculated δ 49 O3 and δ 50 O3 remain >10‰ larger than the measurements (Figure 2). Here, we update previous calculations to include pressure dependence, which reduces δ-values at higher pressures. By incorporating NCEP2 daily temperature into the model, a better agreement is achieved. However, there is a difference between the observed temperature (in situ measurements and NCEP2 data) and the temperature that is required to reproduce the observed values of δ 49 O3 and δ 50 O3 (Table 1 and Figure 3). The in situ measured temperature tends to be higher than the climatological and NCEP2 daily and 6-hourly temperature.        [3]; the low-pressure limit is assumed. T clim , T in situ , and T NCEP are the climatological, in situ measured, and NCEP2 reanalysis daily temperatures, respectively. Zero-point-energy theory for estimating the ozone fractionation in the Chappuis band is applied.

Chappuis Band Photolysis
Photolysis of ozone occurs primarily in the Hartley and Huggins bands in the UV and Chappuis bands at longer wavelengths (450-850 nm). Chappuis band photolysis dominates for altitudes <35 km and could deplete heavy ozone [5,31,32,[41][42][43]. Due to limited photolytic data for major isotopolocules of ozone in the visible band [31,32,44], we followed typical theories to estimate the fractionation. They are either zero-point-energy theory [29] or modified zero-point-energy theory [27,28]. The latter is applied to ozone in the Hartley and Huggins bands and turns out to be reliable [5]. Both theories predict similar and small but positive fractionation in the Chappuis band, and they cannot explain the observed data for 18 [31,32,44]. An alternative way is to scale the fractionation from 18 O 18 O 18 O, and the results obtained by assuming two approaches are shown in Figure 4. One way is to assume that the fractionation is linearly proportional to Atmosphere 2021, 12, 1673 7 of 12 the difference of their zero-point-energies (dashed curves). This approach overestimates the effect from the Chappuis band (see Model C). A factor of four reduction (solid curves) in the zero-point-energy shift provides a better fit to the observations (Model A). However, both produce near-surface ozone isotopically too light compared with the observations (see Figure 1). This discrepancy could be explained by NO + O 3 reaction that enhances the isotopic composition of ozone [45], because the measurements were taken in urban areas, instead of a clean atmosphere, where the Chapman chemistry is not valid. Thus, the isotopic compositions of near-surface ozone are affected by both the photolysis in the Chappuis band and the reaction with NO. To verify the photolytic calculation shown above, we compare the model adopted fractionations with limited data. The result is summarized in Figure 5; we compare with the data from Huang et al. [32] only, because the fractionation factors were obtained at well-defined wavelengths. We see that at the four wavelengths of the measurements, the model needed fractionations deviate significantly from the laboratory data, suggesting To verify the photolytic calculation shown above, we compare the model adopted fractionations with limited data. The result is summarized in Figure 5; we compare with the data from Huang et al. [32] only, because the fractionation factors were obtained at well-defined wavelengths. We see that at the four wavelengths of the measurements, the model needed fractionations deviate significantly from the laboratory data, suggesting hitherto unknown processes in affecting the photolytic process of ozone. We do not have the data at other wavelengths. Thus, the photolysis-induced isotopic fractionation in the Chappuis band remains a solution to the model-observation discrepancy mentioned above. This calls for an urgent need for laboratory measurements at other wavelengths in the Chappuis band, essential for tropospheric chemistry research. The solar radiation at visible wavelengths is affected by multiple scattering [46]. Hence, the photolysis in the Chappuis band in the stratosphere can be significantly enhanced by clouds in the troposphere. We perform an aerosol and cloud scattering calculation, based on Discrete Ordinates Radiative Transfer Program for a Multi-Layered Plane-Parallel Medium [47], by introducing a bright cloud layer between 900-1200 m, with single scattering albedo 0.999 and asymmetry factor 0.85. The typical cloud optical depth at 300 nm is ~18.6, compared to that due to ozone absorption (~3.6) and Rayleigh extinction (~1.3). Figure 1 demonstrates an example of enhancing the photolysis rate coefficient in the Chappuis bands (Model F). Indeed, the model helps reduce the delta values in the lower stratosphere (cf. Model A). We note that cloud multiple scattering is not a solution to the aforementioned model imperfection. Instead, the role of scattering is to amplify the isotopic fractionation in the Chappuis band.

Discussion and Conclusions
It is known that the isotopic composition of O3 is influenced by its formation and photolysis. Here, we focus our analysis and make comparison with ozone measurements from mass spectrometry, because of its analytical precision. Remote sensing data [1,[9][10][11][12], though retrieved at reduced precision, remain potentially useful, especially when retrieval algorithms are improved, because the technique provides good spatial and The solar radiation at visible wavelengths is affected by multiple scattering [46]. Hence, the photolysis in the Chappuis band in the stratosphere can be significantly enhanced by clouds in the troposphere. We perform an aerosol and cloud scattering calculation, based on Discrete Ordinates Radiative Transfer Program for a Multi-Layered Plane-Parallel Medium [47], by introducing a bright cloud layer between 900-1200 m, with single scattering albedo 0.999 and asymmetry factor 0.85. The typical cloud optical depth at 300 nm is 18.6, compared to that due to ozone absorption (~3.6) and Rayleigh extinction (~1.3). Figure 1 demonstrates an example of enhancing the photolysis rate coefficient in the Chappuis bands (Model F). Indeed, the model helps reduce the delta values in the lower stratosphere (cf. Model A). We note that cloud multiple scattering is not a solution to the aforementioned model imperfection. Instead, the role of scattering is to amplify the isotopic fractionation in the Chappuis band.

Discussion and Conclusions
It is known that the isotopic composition of O 3 is influenced by its formation and photolysis. Here, we focus our analysis and make comparison with ozone measurements from mass spectrometry, because of its analytical precision. Remote sensing data [1,[9][10][11][12], though retrieved at reduced precision, remain potentially useful, especially when retrieval algorithms are improved, because the technique provides good spatial and temporal coverages that mass spectrometry cannot. Furthermore, spectroscopic methods distinguish symmetric from asymmetric ozone molecules, essential for identifying missing processes, if they exist, in affecting the isotope composition of ozone in the atmosphere, because of their difference in, for example, altitude dependence [5].
Three factors affect the isotopic composition: pressure, temperature, and photolysis. The in situ measured δ 49 O 3 and δ 49 O 3 values between 20 and 35 km range from 50 to 130‰. Large discrepancies between the measurements and previous models are found (Figures 1  and 2 and Table 1). To account for the observed δ 49 O 3 and δ 50 O 3 , their temperature and pressure dependences are examined. The formation of O 3 at higher pressures reduces the abundance of heavy ozone. However, the pressure in the regions of interest (>20 km) is less than 100 mbar, and the modification is about −5‰ or less, compared with the low-pressure calculation ( Figure 1). Hence, the pressure dependence as a source of the discrepancy seen for the data in the stratosphere is insufficient. The isotopic value of atmospheric O 3 has relatively weak temperature dependence (~0.6‰ K −1 ), and the required temperature to explain the data differs significantly from the reanalysis and in situ temperatures (Table 1). Therefore, the temperature mechanism becomes less plausible. This leaves attenuated dissociative photon flux as the only mechanism, though hitherto unknown mechanisms in fractionating the isotopic composition of O 3 in the atmosphere are not ruled out. As the model values are biased to be too high compared with the measurements, the photolysis in the Chappuis band could help reduce the deviation if the rate coefficient or the isotopic fractionation in this band is enhanced. Calculations of multiple photon scattering that affect dissociative photon distributions are insufficient to reduce the isotopic composition of ozone. Directly tuning the fractionation factor in the Chappuis band provides a better explanation. New laboratory measurements, especially the Chappuis band, are needed to quantify the processes that affect the isotopic composition of ozone in the atmosphere.
The isotopic signature in O 3 can be transferred readily to other trace species such as the hydroxyl radical, nitrate, and nitrite [7,18,19,26,48]. Take NO x (=NO + NO 2 ) as an example. The transfer of isotope anomaly from O 3 to nitrate and nitrite is due to the following reactions: Hence, the anomalous isotope signature in oxygen provides useful tools for tracing pollution chemistry because O 3 is central to tropospheric chemistry [49,50]. In addition to the present-day atmosphere, the composition of paleo-atmospheres could also be constrained by the unique isotope anomaly in oxygen, such as the level of carbon dioxide [51]. The applicability requires the knowledge of processes that affect the isotopic composition of ozone, which remains unsatisfactory. Photolysis in the Chappuis band, in particular, deserves further investigation, because it is essential in affecting the isotopic composition of ozone.